One of our main activities over the last few years has been the development of a comprehensive model for oscillations of membrane potential and calcium on time scales ranging from seconds to minutes. These lead to corresponding oscillations of insulin secretion. The basic hypothesis of the model is that the faster oscillations (tens of seconds) stem from feedback of calcium onto ion channels, likely calcium-activated potassium (K(Ca)) channels and ATP-dependent potassium (K(ATP)) channels, whereas the slower oscillations (five minutes) stem from oscillations in metabolism. The metabolic oscillations are transduced into electrical oscillations via the K(ATP) channels. The model thus consists of an electrical oscillator (EO) and a metabolic oscillator (MO) and is referred to as the Dual Oscillator Model (DOM). In our model, the MO is a glycolytic oscillator, but many of the features of the system would still hold if the metabolic oscillation arose elsewhere, such as the mitochondria. K(ATP) channels are of clinical significance as they are a first-line target of insulin-stimulating drugs, such as the sulfonylureas tolbutamide and glyburide, used in the treatment of Type 2 Diabetes. Severe gain-of-function mutations of K(ATP) are a major cause of neo-natal diabetes mellitus, whereas moderate gain-of-function mutations have been linked in genome-wide association studies (GWAS) to the milder but more common disease, adult-onset type 2 diabetes. Conversely, loss-of-function mutations of K(ATP) are a major cause of familial hyperinsulinism, a hereditary disease found in children in which beta cells are persistently electrically active and secrete insulin in the face of normal or low glucose, causing life-threatening hypoglycemia. During the report period we have published additional evidence supporting the DOM. We measured the conductance of K(ATP) channels by applying voltage ramps to beta cells in mouse islets and measuring the current. The slope of the current-voltage curve gives the conductance by Ohm's law. We found that conductance is lowered during the active phase of the slow oscillations, in agreement with the prediction of the model that a surge of glycolytic activity triggers each active phase. In contrast, other models, in which changes in metabolism, specifically the ATP/ADP ratio, stem from rises in calcium, which activate removal of calcium by ATP-consuming calcium pumps, are not compatible with this observation. In such models, the rise in calcium during the active phase predicts a reduction in the ATP/ADP ratio and an increase in K(ATP) conductance, opposite to what we observed. That role of calcium may still be an important contributor to the fast oscillations. This work is described in Ref. # 1. A third, previously unappreciated mode of oscillation, in which neither metabolism alone can drive calcium oscillations nor can calcium alone drive metabolic oscillations was uncovered by a detailed mathematical analysis of the DOM. In this mode, a transient increase in glycolytic activity raises calcium, and the transient rise in calcium triggers the next glycolytic spike by depleting ATP. Together, the two can produce a sustained oscillation. This shed new light on findings described in the 2012 report showing that metabolic oscillations (assessed by measuring NAD(P)H) can sometimes persist in the absence of calcium oscillations but sometimes are terminated. It is possible that the latter case reflects the third mode of oscillation in which metabolic oscillations cannot occur in the absence of calcium oscillations. This work is described in Ref. # 4. We also initiated a new project on modeling pancreatic alpha cells, which oppose the action of beta cells by secreting glucagon; whereas insulin lowers glucose, glucagon increases it. Consequently, glucagon secretion is also responsive to plasma glucose but in the opposite direction - secretion is highest when glucose is low. This has clinical relevance to both type 1 and type 2 diabetes, where inappropriate glucagon secretion exacerbates the symptoms of the disease. In these patients, too much glucagon is secreted at high glucose, worsening the hyperglycemia, and too little glucagon is secreted at low glucose, increasing the risk of hypoglycemia. The latter is particularly dangerous for patients who have to inject insulin and are often subject to episodes of severe hypoglycemia, which increases both morbidity and mortality. Our work has focused on how the electrical and secretory activity of alpha cells is regulated by glucose, which is a puzzle given that alpha cells have a very similar metabolically regulated K(ATP) channel system as beta cells. We tested two prevailing theories from the literature. One proposes that increased membrane potential due to K(ATP) channel closure reduces secretion because of voltage-dependent inactivation of calcium and sodium channels. The other proposes that increased ATP fills the endoplasmic reticulum calcium store and turns off a stimulatory store-operated current (SOC). We showed with the model that both mechanisms can work, but that the response is a bell-shaped curve. This agrees with experimental findings and, more important, implies that increased glucose (decreased K(ATP) conductance) can either increase or decrease glucagon secretion, depending on where the cell sits on the curve initially. We believe this accounts for much of the divergence in the literature of alpha-cell responses to glucose; these data are not contradictory but rather reflective of heterogeneity of K(ATP) and SOC expression. We also showed that by combining the two mechanisms we can account for the paradoxical J-shaped dose response curve to glucose - as glucose is increased from about 1 mM to 6 mM, glucagon secretion decreases, but further increases in glucose cause glucagon secretion to increase. Neither mechanism by itself can produce such behavior as the bell-shaped curves bend the wrong way. This work is described in Ref. # 3. Future work will build on this model to study how alpha and beta cells interact via their secreted hormones to coordinate their activity. With the help of a group of students in the Research Experience for Undergraduates (REU), we have developed an efficient computational platform based on Matlab to calculate interactions among islet cells. This work is described in Ref. # 2.